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Is the boundary of a Siegel disk a Jordan curve?


Author: James T. Rogers
Journal: Bull. Amer. Math. Soc. 27 (1992), 284-287
MSC (2000): Primary 30C35; Secondary 30D45, 54F15
DOI: https://doi.org/10.1090/S0273-0979-1992-00324-5
MathSciNet review: 1160003
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Abstract: Bounded irreducible local Siegel disks include classical Siegel disks of polynomials, bounded irreducible Siegel disks of rational and entire functions, and the examples of Herman and Moeckel. We show that there are only two possibilities for the structure of the boundary of such a disk: either the boundary admits a nice decomposition onto a circle, or it is an indecomposable continuum.


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Additional Information

DOI: https://doi.org/10.1090/S0273-0979-1992-00324-5
Keywords: Siegel disk, Julia set, Fatou set, indecomposable continuum, prime end
Article copyright: © Copyright 1992 American Mathematical Society

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